SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 937-964, January 2020.
We study the problem of minimizing the discounted probability of exponential Parisian ruin, that is, the discounted probability that an insurer's surplus exhibits an excursion below zero in excess of an exponentially distributed clock. The insurer controls its surplus via reinsurance priced according to the mean-variance premium principle, as in Liang, Liang, and Young [Optimal Reinsurance Under the Mean-Variance Premium Principle to Minimize the Probability of Ruin, Working paper, Department of Mathematics, University of Michigan, 2019]. We consider the classical risk model and apply stochastic Perron's method, as introduced by Bayraktar and Sîrbu [Proc. Amer. Math. Soc., 140(2012), pp. 3645--3654; SIAM J. Control Optim., 51(2013), pp. 4274--4294; Proc. Amer. Math. Soc., 142(2014), pp. 1399--1412], to show that the minimum discounted probability of exponential Parisian ruin is the unique viscosity solution of its Hamilton--Jacobi--Bellman equation with boundary conditions at $\pm \infty$. A major difficulty in proving the comparison principle arises from the discontinuity of the Hamiltonian.

中文翻译：

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通过再保险最大限度地降低指数巴黎废墟的折现概率

SIAM控制与优化杂志，第58卷，第2期，第937-964页，2020年1月。
我们研究了使指数式巴黎废墟的折现概率最小化的问题，换句话说，就是保险人的盈余在指数分布时钟之外的零下出现偏移的折现概率。保险公司通过根据均值方差保费原理定价的再保险来控制其盈余，如Liang，Liang和Young [在均值方差保费原理下的最佳再保险以使破产概率最小化，工作论文，大学数学系密歇根州，2019年]。我们考虑了经典的风险模型，并采用了Bayraktar和Sîrbu[Proc。阿米尔。数学。Soc。，140（2012），第3645--3654页; SIAM J.Control Optim。，51（2013），第4274--4294页; 进程 阿米尔。数学。Soc。，142（2014），第1399--1412页]，证明指数巴黎废墟的最小折现概率是其边界条件为$ \ pm \ infty $的Hamilton-Jacobi-Bellman方程的唯一粘性解。证明比较原理的主要困难来自哈密顿量的不连续性。